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Theorems · Definition · commutative algebra

MvPolynomial.weightedGradedAlgebra

(R : Type u_1) →
  {M : Type u_2} →
    [inst : CommSemiring R] →
      {σ : Type u_3} →
        (w : σ → M) →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : DecidableEq M] → GradedAlgebra (MvPolynomial.weightedHomogeneousSubmodule R w)

Given a weight, MvPolynomial as a graded algebra

Defined in
Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous
Cited by
2 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringAddCommMonoidDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPolynomial.mem_iff_weightedHomogeneousComponent_mem · cited by 2MvPolynomial.mem_iff_weig…MvPolynomial.weightedHomogeneousComponent_mem_of_mem · cited by 1MvPolynomial.weightedHomo…AddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringFinsupp · cited by 5255FinsuppMvPolynomial · cited by 2140MvPolynomialGradedAlgebra · cited by 97GradedAlgebraDirectSum.Decomposition · cited by 57DirectSum.DecompositionSetLike.GradedMonoid · cited by 48SetLike.GradedMonoidMvPolynomial.weightedHomogeneousSubmodule · cited by 23MvPolynomial.weightedHomo…MvPolynomial.weightedDecomposition · cited by 2MvPolynomial.weightedDeco…MvPolynomial.WeightedHomogeneousSubmodule.gradedMonoid · cited by 1WeightedHomogeneousSubmod…MvPolynomial.weightedGradedAl…CITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.